In this section we review existing results on variable clustering that will be used throughout this paper. If model (REF ) is used as a background for defining
clusters of variables, then [1]} showed that these clusters are uniquely defined, up to label switching, as soon as \(m=: \min _{1 \le k \le K} |G_k^*| \ge 2\)  and the components of the latent vector \(\)  are different a.s. :
\(\Delta (_{  }^*)=: \min _{j < k} (Z_j - Z_k)^2 > 0.\) 
